A solar radio moving type Ⅳ burst of expanding arches type involving multi-sources

A complex solar radio moving type IV burst was observed on 23 September 1998 with the broadband (1.0-2.0 GHz and 2.6-3.8 GHz) spectrometers with high temporal and spectral resolutions at National Astronomical Observatories of China (NAOC). Comparing to the high spatial resolution data of Siberian Solar Radio Telescope (SSRT), we find that this burst is a rare type of moving type IV burst which is caused by the expanding arches, and the spatial structure oscillations of the radio sources are related with the time structure pulsations of the radio emission. Furthermore, the burst is associated with the multiple quasi-periodic long-term pulsations, and this suggests the existence of multi-scale magnetic structures in a large expanding coronal arch. We think the moving type IV burst is due to the synchrotron emission of the energetic electrons trapped in the expanding arch, and the multiple quasi-periodic pulsations are due to the second harmonic plasma emission.     

Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations

The effect of periodic forcing and impulsive perturbations on predator–prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade.     

Interpretation of solar microwave C type burst spectra in terms of magnetic nonhomogeneity

The solar radio spectra of the gyro-synchrotron radiation without absorption from mildly relativistic non-thermal electron have been presented using the model with the spherical symmetric nonhomogeneity. These spectra have the following features: (i) Twists and turns of the spectra, which appear at the joint between the medium and high frequencies, (ii) Flux density drop at the lower frequencies. Even if there are no absorption in the radio sources, flux density drop at the lower frequencies is still present because of magnetic nonhomogeneity. (iii) These theoretical spectra belong to C type. This provides us a new interpretation for the observed solar burst C type spectra. Project supported by the National Natural Science Foundation of China.     

A pair of solar spike emissions

Using the 2.6–3.8 GHz solar radio spectrometer of the National Astronomical Observatories of China (NAOC), a pair of microwave millisecond spike (MMS) emissions were observed, and their frequency drift rate was measured. The separatrix frequency of the MMS pair was at 2900 MHz. Its emission layer was about 2×10⁴km above the photosphere. The polarization degree was wave-like variation with an average value of about 25% in LCP. An MMS pair differs greatly from the type III bursts pair. For the latter, in a certain frequency range, there is no emission around separatrix frequency. This phenomenon may help better understand the mechanism of MMS.     

On the spectral study of sunspot number and solar radio flux between 600 and 9400 MHz

The relationship between the solar activity, as represented by sunspot number and the slowly varying component of solar radio emission at frequencies from 600 to 9400 MHz, has been sudied for high solar activity (1957–58), declining phase of moderate solar activity (1961–62) and ascending phase of moderate solar activity (1965–66). Regression and auto-spectrum analyses show that the association of the slowly varying radio emissions with sunspot activity is best around 3750 MHz for high solar activity period, around 2800 MHz for moderate activity during the declining phase and in between 2800 and 3750 MHz for ascending phase of activity. The coherence between radio flux at frequencies from 600 MHz to 9400 MHz was high and free from large fluctuations upto wavelengths as short as 7 days in the year 1961–62. At 9400 MHz, however, it is high and steady for wavelengths in excess of about 15 days. At solar synodic rotation period the phase difference between the sunspot number and the slowly varying component shows little change with the wavelength of the radio emission.     

A pair of solar spike emissions

Using the 2.6-3.8 GHz solar radio spectrometer of the National Astronomical Observatories of China (NAOC), a pair of microwave millisecond spike (MMS) emissions were observed, and their frequency drift rate was measured. The separatrix frequency of the MMS pair was at 2900 MHz. Its emission layer was about 2×104km above the photosphere. The polarization degree was wave-like variation with an average value of about 25% in LCP. An MMS pair differs greatly from the type III bursts pair. For the latter, in a certain frequency range, there is no emission around separatrix frequency. This phenomenon may help better understand the mechanism of MMS.     

An adaptive algorithm in time domain for dynamic analysis of a simply supported beam subjected to a moving vehicle

This paper presents an adaptive algorithm in the time domain for the dynamic analysis of a simply supported beam subjected to the moving load and moving vehicle with/without varying surface roughness. By expanding variables at a discretized time interval, a coupled spatial‐temporal problem can be converted into a series of recursive space problems that are solved by finite element method (FEM), and a piecewised adaptive computing procedure can be carried out for different sizes of time steps. The proposed approach is numerically verified via the comparison with analytical and the Runge–Kutta method‐based solutions, and satisfactory results have been achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiple positive periodic solutions of a delayed discrete predator–prey system with type IV functional responses

In this paper, a discrete periodic predator–prey system with type IV functional responses and time delay is investigated. Using Gaines and Mawhin’s continuation theorem from coincidence degree theory as well as some prior estimates, we get sufficient conditions for the existence of positive periodic solutions of the system. This is also the first time that the coincidence degree theory has been used to obtain multiple positive periodic solutions in discrete ecological systems.     

Singularity of homogeneous Einstein metrics

We examine homogeneous cosmological models with arbitrary (uniform) motion of matter. We have shown the presence of an oscillatory mode of the BLK type when moving toward a cosmological singularity in models of II–IV and VI–IX Bianchi types. We have formulated constraints on the velocities under which the oscillatory mode degenerates to Kästner asymptotics.     

Poincaré–Treshchev Mechanism in Multi-scale,Nearly Integrable Hamiltonian Systems

This paper is a continuation to our work (Xu et al. in Ann Henri Poincaré 18(1):53–83, 2017) concerning the persistence of lower-dimensional tori on resonant surfaces of a multi-scale, nearly integrable Hamiltonian system. This type of systems, being properly degenerate, arise naturally in planar and spatial lunar problems of celestial mechanics for which the persistence problem ties closely to the stability of the systems. For such a system, under certain non-degenerate conditions of Rüssmann type, the majority persistence of non-resonant tori and the existence of a nearly full measure set of Poincaré non-degenerate, lower-dimensional, quasi-periodic invariant tori on a resonant surface corresponding to the highest order of scale is proved in Han et al. (Ann Henri Poincaré 10(8):1419–1436, 2010) and Xu et al. (2017), respectively. In this work, we consider a resonant surface corresponding to any intermediate order of scale and show the existence of a nearly full measure set of Poincaré non-degenerate, lower-dimensional, quasi-periodic invariant tori on the resonant surface. The proof is based on a normal form reduction which consists of a finite step of KAM iterations in pushing the non-integrable perturbation to a sufficiently high order and the splitting of resonant tori on the resonant surface according to the Poincaré–Treshchev mechanism.     

Friction induced flutter instability - on modeling and simulation of brake-squeal -

The issue of this contribution are self–excited vibrations due to sliding friction between moving elastic bodies. Starting from Hamiltons principle, the normal contact is implemented by two different approaches. Assuming discretizations in a spatial coordinate frame, the structure of the resulting equations of motions is outlined. For a simple model of a disc–brake, stability charts of the steady–state are presented, which show a considerable influence of the motion of the disc on the stability behavior. Finally, the influence of penalty approaches to the normal contact is addressed shortly. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiple periodic solutions of delayed predator–prey systems with type IV functional responses

In this paper, we considered a periodic predator–prey system with a type IV functional response, which incorporates the periodicity of the environment. Sufficient conditions for the existence of multiple positive periodic solutions are established by applying the continuation theorem. This is the first time that multiple periodic solutions are obtained by using the theory of coincidence degree. Moreover, unlike other types of functional responses, a type IV functional response declines at high prey densities. Thus the existing arguments for obtaining bounds of solutions to the operator equation Lx=λNx are inapplicable to our case and some new arguments are employed for the first time.     

An autonomous system with attractor of Smale–Williams type with resonance transfer of excitation in a ring array of van der Pol oscillators

An autonomous system we propose is a ring structure of a large number of van der Pol oscillators, which manifests cyclic propagation of the localized excitation with phase undergoing the expanding circle map transformation on each full revolution. Due to this, it is reasonable to suppose that attractor of Smale–Williams type occurs in the phase space of the system. Because of the slow spatial variation of the natural frequencies of the oscillators around the ring, it appears possible to exploit resonance mechanism for the excitation transfer; so, the system may have prospects for implementation of high-frequency chaos generators.     

Moving gap solitons in periodic potentials

We address the existence of moving gap solitons (traveling localized solutions) in the Gross–Pitaevskii equation with a small periodic potential. Moving gap solitons are approximated by the explicit solutions of the coupled‐mode system. We show, however, that exponentially decaying traveling solutions of the Gross–Pitaevskii equation do not generally exist in the presence of a periodic potential due to bounded oscillatory tails ahead and behind the moving solitary waves. The oscillatory tails are not accounted in the coupled‐mode formalism and are estimated by using techniques of spatial dynamics and local center‐stable manifold reductions. Existence of bounded traveling solutions of the Gross–Pitaevskii equation with a single bump surrounded by oscillatory tails on a large interval of the spatial scale is proven by using these techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy

We study the existence of quasi-periodic, invariant tori in a nearly integrable Hamiltonian system of high order proper degeneracy, i.e., the integrable part of the Hamiltonian involves several time scales and at each time scale the corresponding Hamiltonian depends on only part of the action variables. Such a Hamiltonian system arises frequently in problems of celestial mechanics, for instance, in perturbed Kepler problems like the restricted and non-restricted 3-body problems and spatial lunar problems in which several bodies with very small masses are coupled with two massive bodies and the nearly integrable Hamiltonian systems naturally involve different time scales. Using KAM method, we will show under certain higher order non-degenerate conditions of Bruno–Rüssmann type that the majority of quasi-periodic, invariant tori associated with the integrable part will persist after the non-integrable perturbation. This actually concludes the KAM metric stability for such a properly degenerate Hamiltonian system.     

Nonlinear dynamics of a simplified engine-propeller system

This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge–Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.     

On Quasi-Periodic Solutions of Differential Equations with Piecewise Constant Argument

We study the existence of quasi-periodic solutions to differential equations with piecewise constant argument (EPCA, for short). It is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. The appearance of quasi-periodic rather than periodic solutions is due to the piecewise constant argument. This new phenomenon illustrates a crucial difference between ODE and EPCA. The results are extended to nonlinear equations.     

Quasi-periodic solutions of nonlinear Schrödinger equations of higher dimension

It is shown that there are plenty of quasi-periodic solutions of nonlinear Schrödinger equations of higher spatial dimension, where the dimension of the frequency vectors of the quasi-periodic solutions are equal to that of the space.     

Solitary wave solutions for a general Boussinesq type fluid model

The possible solitary wave solutions for a general Boussinesq (GBQ) type fluid model are studied analytically. After proving the non-Painlevé integrability of the model, the first type of exact explicit travelling solitary wave with a special velocity selection is found by the truncated Painlevé expansion. The general solitary waves with different travelling velocities can be studied by casting the problems to the Newtonian quasi-particles moving in some proper one dimensional potential fields. For some special velocity selections, the solitary waves possess different shapes, say, the left moving solitary waves may possess different shapes and/or amplitudes with those of the right moving solitons. For some other velocities, the solitary waves are completely prohibited. There are three types of GBQ systems (GBQSs) according to the different selections of the model parameters. For the first type of GBQS, both the faster moving and lower moving solitary waves allowed but the solitary waves with“middle” velocities are prohibit. For the second type of GBQS all the slower moving solitary waves are completely prohibit while for the third type of GBQS only the slower moving solitary waves are allowed. Only the solitary waves with the almost unit velocities meet the weak non-linearity conditions.